Abstract:
The beliefs and "misconceptions" held by learners of elementary mathematics are well researched and documented. Theories about how these ideas change through experience and discussion with others have been developed over many years, and several theories highlight the role of cognitive conflict.
The paper will discuss ways currently being explored of using computer-based modelling systems as a neutral but authoritative participant in a process by which cognitive conflict is generated and resolved by learners. The research highlights the computer's ability to reveal learners' mathematical beliefs and thought processes in a dynamic and visual way which can support articulation and challenge by the teacher and by peers. This feature may help improve our knowledge of how cognitive restructuring occurs, and ways of recording evidence about the change process, rather than just measuring the extent of change, will be discussed.
The paper will discuss ways currently being explored of using computer-based modelling systems as a neutral but authoritative participant in a process by which cognitive conflict is generated and resolved by learners. The research highlights the computer's ability to reveal learners' mathematical beliefs and thought processes in a dynamic and visual way which can support articulation and challenge by the teacher and by peers. This feature may help improve our knowledge of how cognitive restructuring occurs, and ways of recording evidence about the change process, rather than just measuring the extent of change, will be discussed.